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Geometrical equivalence, geometrical similarity, and geometrical compatibility of algebras. (English) Zbl 1139.08004
Zap. Nauchn. Semin. POMI 330, 201-222 (2006) and J. Math. Sci., New York 140, No. 5, 716-728 (2006).
From the introduction: In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
This paper is the full text of the talk, given at the 21st of September, 2002, in St. Petersburg. Most of the proofs are contained in the paper [Proc. Steklov Inst. Math. 242, 165–196 (2003) and Tr. Mat. Inst. Im. V. A. Steklova 242, 176–207 (2003; Zbl 1062.08012)]. The present paper is shorter and reflects the general picture in more clear and compact way. It also contains some proofs which are absent in [loc. cit.]. Besides, we formulate a list of problems, stimulated by the idea of coincidence of geometries.

08B99 Varieties
14A22 Noncommutative algebraic geometry
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